Question

In a triangle ABC, $\angle B=\angle C$ and angle $\text{A}=\text{1}{{00}^{\circ }}$. Find the measure of angle B.

Answer 1

Hint:At first, consider the value of angle B as x, so one can say that angle C is equal to x as angle B is equal to angle C. Thus, one can use the property that, the sum of angles of the triangle is ${{180}^{\circ }}$ to find the value of x, thus the value of angle B.

Complete step by step answer:
In the question, we are given a triangle ABC in which we are said that the measure of angle A is ${{100}^{\circ }}$. We are further said that the measure of angle B is equal to the measure of angle C and thus from this, we have to find a measure of angle B.
So, as we are given the value of A as ${{100}^{\circ }}$ and the value of angle B is equal to angle C. So, we can suppose or let's consider that, the value of angle B be x. So, as both the value of angle B and angle C is equal. So, we can say the value of angle C is x too.
Hence, we can draw a figure of triangle ABC to represent its angles. So, we get:

Here, now we will apply the property of angles in a triangle that is sum of angles of triangle is ${{180}^{\circ }}$ so we can say that,
\[\angle A+\angle B+\angle C={{180}^{\circ }}\]
So on substituting angle A as ${{100}^{\circ }}$ and angle B and C as x, we get:
\[\begin{align}
  & {{100}^{\circ }}+x+x={{180}^{\circ }} \\
 & \Rightarrow {{100}^{\circ }}+2x={{180}^{\circ }} \\
\end{align}\]
Now subtracting ${{100}^{\circ }}$ from both sides we get:
\[\begin{align}
  & {{100}^{\circ }}+2x-{{100}^{\circ }}={{180}^{\circ }}-{{100}^{\circ }} \\
 & \Rightarrow 2x={{80}^{\circ }} \\
\end{align}\]
Hence the value of x is $\dfrac{{{80}^{\circ }}}{2}\Rightarrow {{40}^{\circ }}$
Thus, the value of angle B is ${{40}^{\circ }}$

Note:
 From the angles also, we can say certain properties which it depicts such as, if two angles are equal then we can say that their sides opposite to equal angles are also equal. Let's say in question angle B is equal to angle C so we can say AC is equal to AB. It is important to draw a fig and mark all the angles, such that students can easily identify angle B, and hence it's the measure.